Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems

We investigate a 1D disordered Hamiltonian with a non analytical step-like dispersion relation whose level statistics is exactly described by Semi-Poisson statistics(SP). It is shown that this result is robust, namely, does not depend neither on the microscopic details of the potential nor on a magnetic flux but only on the type of non-analyticity. We also argue that a deterministic kicked rotator with a non-analytical step-like potential has the same spectral properties. Semi-Poisson statistics (SP), typical of pseudo-integrable billiards, has been frequently claimed to describe critical statistics, namely, the level statistics of a disordered system at the Anderson transition (AT). However we provide convincing evidence they are indeed different: each of them has its origin in a different type of classical singularities.Comment: typos corrected, 4 pages, 3 figure

Symmetry limit properties of a priori mixing amplitudes for non-leptonic and weak radiative decays of hyperons

We show that the so-called parity-conserving amplitudes predicted in the a priori mixing scheme for non-leptonic and weak radiative decays of hyperons vanish in the strong-flavor symmetry limit

A semiclassical theory of the Anderson transition

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality, $d$. The critical exponent $\nu$ controlling the divergence of the localization length at the transition is found to be $\nu = {1 \over 2}+ {1 \over {d-2}}$. This result confirms that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality.Comment: 4 pages, journal versio

Anderson transition in systems with chiral symmetry

Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry.Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references, final version as published in Phys. Rev.

Multi-sensor system using plastic optical fibers for intrinsically safe level measurements

A system for measuring liquid level in multiple tanks using optical fibe technology has been developed. Oil fiel service industry or any sector requiring liquid level measurements in flammabl atmospheres can be benefite from this intrinsically safe technology. The device used a single lens for the emitting and receiving fibe and it is based on amplitude variations as a function of the liquid distance and not in time of fligh or phase detection. Being the firs fiber-opti liquid level sensor with those characteristics for long ranges (>200 cm). A simple model to describe their behavior has been derived and tested on two prototypes. A Monte-Carlo method is used to fi the experimental data and obtain the model parameters. High accuracy between experimental data and fitte curve is obtained. The prototypes have a good linearity, better than 1.5% FS (full scale). Sensor heads are made of plastic optical fiber (POF) that are easy to handle, flexible and economical. They are excited by 650 nm lasers, housed in ST-connectors to obtain compact and rough prototypes. Optical multiplexing is used to increase the measuring safety area. Frequency division multiplexing is used to address each sensor head. A discussion about the influenc of tilts and aberrations is also included.Publicad

Marginal and irrelevant disorder in Einstein-Maxwell backgrounds

We study analytically the effect of a weak random chemical potential of zero average in an Einstein-Maxwell background. For uncorrelated disorder this perturbation is relevant however we show that it can become marginal or even irrelevant by tuning disorder correlations. At zero temperature we find that, to leading order in the disorder strength, the correction to the conductivity for irrelevant perturbations vanishes. In the marginal case, in order to renormalize a logarithmic divergence, we carry out a resummation of the perturbative expansion of the metric that leads to a Lifshitz-like geometry in the infrared. Disorder in this case also induces a positive correction to the conductivity. At finite temperature the black hole acquires an effective charge and the thermal conductivity has the expected Drude peak that signals the breaking of translational invariance. However the electric conductivity is not affected by the random chemical potential to leading order in the disorder strength.A. M. G. thanks Hong Liu and Elias Kiritsis for illuminating discussions. A. M. G. acknowledges partial support from EPSRC, grant No. EP/I004637/1. B. L. thanks Andrew Lucas for interesting discussions and suggestions concerning the conductivity. B.L. is supported by a CAPES/COT grant No. 11469/13-17. Both authors are grateful to the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society